Equations — O/L Mathematics

How do I practise Equations?

3 questions with worked solutions

1. Solve the equation: (2x + 1)/3 + (x - 2)/4 = 3. Show all your working.
   Show worked solution

   LCM of 3 and 4 is 12. Multiply every term by 12: 12*(2x+1)/3 + 12*(x-2)/4 = 12*3 => 4(2x+1) + 3(x-2) = 36. Expand: 8x + 4 + 3x - 6 = 36 => 11x - 2 = 36 => 11x = 38 => x = 38/11. Check: (2*(38/11)+1)/3 + (38/11 - 2)/4 = (76/11 + 1)/3 + (38/11 - 22/11)/4 = (87/11)/3 + (16/11)/4 = 87/33 + 16/44 = 29/11 + 4/11 = 33/11 = 3. Correct.
   Modelled on: the O/L Mathematics examination pattern
2. Solve the simultaneous equations: 3x + 2y = 16 and 5x - 3y = -5.
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   Multiply first equation by 3: 9x + 6y = 48. Multiply second equation by 2: 10x - 6y = -10. Add: 19x = 38 => x = 2. Substitute x=2 into 3x+2y=16: 6 + 2y = 16 => 2y = 10 => y = 5. Check in second: 5(2) - 3(5) = 10 - 15 = -5. Correct.
   Modelled on: the O/L Mathematics examination pattern
3. Solve the quadratic equation: 2x² - 7x + 3 = 0 by factoring.
   Show worked solution

   ac = 2*3 = 6. Find two numbers multiplying to 6 and adding to -7: -6 and -1. Split middle term: 2x² - 6x - x + 3 = 0. Group: 2x(x - 3) -1(x - 3) = 0 => (2x - 1)(x - 3) = 0. Set each factor to zero: 2x - 1 = 0 => x = 1/2; x - 3 = 0 => x = 3. Roots: x = 1/2 or x = 3.
   Modelled on: the O/L Mathematics examination pattern

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Where does Equations fit in the syllabus?

Grade 10 · Term 2 · Grade 11 · Term 2